OEIL Manual. Interconnect Design. Sensitivity Analysis. Attenuation Analysis. Crosstalk Noise Analysis. Bandwidth Density

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1 OEIL Manual Version 3.0 December 2015 Optical/Photonic Technology for Interconnected Computing System Lab Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology eexu Interconnect Design OEIL Device Library Crosstalk Noise Analysis Attenuation Analysis Sensitivity Analysis Power Consumption Analysis Area Analysis Bandwidth Analysis Latency Analysis Crosstalk Noise Coefficienct Attenuation& Sensitivity Energy Efficiency Area Bandwidth Density Latency Figure 1: The flow chart of OEIL simulator. 1

2 CONTENTS 1 Introduction 3 2 How to Use OEIL Usage Instructions The Parameter File The Configuration File The Output File Models for Optical Interconnect Crosstalk Noise Attenuation Receiver Sensitivity Energy Consumption Bandwidth Density Latency Notation Table Models for Electrical Interconnect Crosstalk Noise Attenuation Receiver Sensitivity Energy Consumption Bandwidth Density Latency Notation Table Models for Serializers and Deserializers SerDes Modelling Energy Efficiency and area Latency Notation Table Reference 18 Version History 18 2

3 1 INTRODUCTION OEIL is an analysis tool for optical and electrical interfaces and links. Fig. 1 illustrates the internal structure of OEIL. The publicly released OEIL is implemented in C code, and it is available online with documentation at [1]. OEIL has a complete library of devices for inter-chip interconnects. It analyzes power consumptions, energy efficiencies, bandwidths, bandwidth densities and latencies of optical and electrical inter-chip interconnects. As can be seen from the figure, the main body of OEIL includes models for crosstalk noises, attenuations, receiver sensitivities, power consumptions, bandwidths and latencies. This tool is designed based on the proposed analytical models in previous sections. The input files of tool OEIL include interconnect configurations and device parameters, and the output results are written in output. The configurations of interconnects such as data rate, interconnect length and number of parallel interconnects are described in file interconnect configurations. The parameters of board, microresonator, trace, waveguide, transmitter and receiver can be found in file device parameters. Those files have two versions, which are differed by key words electrical and optical. In additional to the above results, OEIL also generates the intermediate results of analytical models such as crosstalk talk coefficients, attenuations, and receiver sensitivities. OEIL evaluates the performance of inter-chip interconnects from end to end, which consists of on-chip interconnect, off-chip interconnect and interfaces between them [2]. For electrical interconnects, the device library includes parameters of wires on chip, traces on board as well as electrical copper pins. For optical interconnects, the device library includes parameters of silicon waveguides on chip, polymer waveguides on board, and optical lens or couplers. Additionally, OEIL is also able to evaluate the performance of interconnects, which connect 2.5D or 3D chips. The device library includes parameters of through-silicon vias (TSVs) and bumps among stacked dies. Configurations of the 2.5D or 3D chip can be defined on the configuration file. This tool OEIL is able to not only analyze the performance of inter-chip interconnects but also provide necessary parameters for system simulators. The configuration file is able to describe all kinds of interconnects in a network. OEIL is verified by data from previous published technical reports. It shows good fitting between OEIL and the collected data. The verification will be discussed with more details in next subsection. By updating the device library, OEIL is able to follow the development of technologies. The optical transmission systems are promising candidates for high speed inter-chip interconnects, and have been implemented in various prototypes. In optical interconnect, signals at different wavelengths will not interfere with each other, the wavelength-division multiplexing (WDM) technology are used, which multiplexes a number of signals at different wavelengths in a single optical waveguide. This technology could effectively increase the total bandwidth of optical interconnects. We mathematically build models for their crosstalk noises, attenuations and receiver sensitivities, and use three parameters to compare the performance of inter-chip interconnects: energy consumption, bandwidth density and latency. In our input files, we make assumptions of various parameters based on the state-of-the-art technologies. They could also be modified according to the real systems configured by users. The output file of this simulator covers the most important information of optical interconnects. 3

4 2 HOW TO USE OEIL Before running this simulator, users could modify the parameter file and configuration file in the input folder. Please follow the instructions in this chapter, compile and run the software. The calculated results could be obtained from the result file in the output folder. Enter the directory Compile the software Run the software 2.1 USAGE INSTRUCTIONS cd./oeilv3.0/source g++ OEIL.c -o OEIL -lm./oeil 2.2 THE PARAMETER FILE The program would load the parameter file in order to build models for optical devices. The relationship between parameters and notations are listed in Table 1. The parameter file includes optical and electrical sections. File path:./source/parameter_optical.txt #transmitter# 0.2 laser_slope_efficiency n/a //slope efficiency of laser 1 laser_threshold_current ma //threshold current of laser 0.1 laser_extinction_ratio n/a //extinction ratio of laser 900 laser_area um 2 //area of laser 3 laser_voltage V //supply voltage of laser 1.5 driver_voltage V //supply voltage of driver #waveguide# 0.35 optical_pin_loss n/a //coupling efficiency of pin 250 optical_pin_height um //height size of pin 250 optical_pin_width um //width size of pin propagation_loss cm 1 //propagation loss of pin 1.55 wg_refractive_index n/a //refractive index of waveguide 62.5 wg_pitch um //The pitch of waveguide #receiver# 14.1 signal_to_noise_ratio n/a //signal to noise ratio 10 tia_noise_density pa Hz //noise density of TIA 1 tia_transimpendance kω //transimpendance of TIA 10 la_voltage_threshold mv //threshold voltage of LA 1 pd_responsity A/W //responsity of PD 60 pd_capacitance ff //input capacitance of PD 4

5 #microresonator# 10 mr_radius_range um //estimated radius of MR mr_attenuation n/a //round trip attenuation of ring 0.3 mr_power_split_k n/a //power split ratio into ring 2.65 mr_refractive_index n/a //refractive index of ring 0.05 mr_tuning_power mw //tuning power of MR 0.12 mr_static_power mw //static power of MR 0.12 mr_dynamic_power mw/gbps //dynamic power of MR 125 mr_area um 2 //area of MR #serdes# 0.1 serdes_cur_optical ma/gbps //unit current of SerDes circuit 40 serdes_area_optical um 2 /Gbps //unit area of SerDes circuit File path:./source/parameter_electrical.txt #board# 17.4 pcb_layer_height mil //height of pcb layer 4 pcb_trace_width mil //width of pcb trace 1.4 pcb_trace_height mil //height of pcb trace 24.0 pcb_trace_pair_pitch mil //pitch of pcb trace pair pcb_trace_loss_tangent n/a //loss tangent of pcb trace 3.6 pcb_dielectric n/a //dielectric of pcb material 1 package_pin_pitch n/a //pitch of package pin #trace# 13.8 trace_half_depth_f MHz //half depth frequency of trace 64.4 trace_characteristic_z Ohm //characteristic res. of trace trace_unit_length_c pf/cm //unit length cap. of trace trace_direct_current_r Ohm //direct current res. of trace 104 trace_input_impendance Ohm //input impendance of trace 1 electrical_pin_load_c pf //cap. of electrical pin load #transceiver# 10 la_threshold_voltage mv //threshold voltage of amplifier 0.05 la_offset_coefficent n/a //offset coefficient of amplifier 0.01 la_coefficent_margin n/a //coefficent margin of amplifier 1.5 circuit_voltage V //supply voltage of circuit #serdes# 0.1 serdes_cur_electrical ma/gbps //unit current of SerDes circuit 40 serdes_area_electrical um 2 /Gbps //unit area of SerDes circuit 5

6 2.3 THE CONFIGURATION FILE The program would load the configuration file in order to build models for optical devices. The relationship between configurations and notations are listed in Table 1. The configuration file includes optical and electrical sections. File path:./source/configuration_optical.txt 10 data_rate_optical GHz //bandwidth of one opti. signal 25 length_optical cm //length of opti. interconnect 8 serdes_ratio_optical n/a //serdes ratio of serdes 8 number_of_wavelengths n/a //number of wavelengths 1550 laser_wavelength nm //laser working wavelength 0 is_direct_modulation n/a //if it is directly modulated File path:./source/configuration_electrical.txt 10 data_rate_electrical Gbps //bandwidth of one elec. signal 40 length_electrical cm //length of elec. interconnect 8 serdes_ratio_electrical n/a //serdes ratio of serdes 8 number_of_pairs n/a //number of trace pairs 2.4 THE OUTPUT FILE The program would output the result file after calculation. The file includes both the intermediate results as well as the final results obtained from our models. The output file includes optical and electrical sections. File path:./source/output_optical.txt sensitivity_oma mw //receiver sensitivity crosstalk_coefficient n/a //crosstalk noise coefficient total_attenuation n/a db //total attenuation energy_consumption pj/bit //energy consumption area_density Gbps/mm 2 //area bandwidth density linear_density Gbps/mm //linear bandwidth density area mm 2 //area latency ns //latency File path:./source/output_electrical.txt sensitivity_la mw //receiver sensitivity crosstalk_coefficient n/a //crosstalk noise coefficient total_attenuation n/a db //total attenuation energy_consumption pj/bit //energy consumption area_density Gbps/mm 2 //area bandwidth density linear_density Gbps/mm //linear bandwidth density area mm 2 //area latency ns //latency 6

7 3 MODELS FOR OPTICAL INTERCONNECT We build models for the crosstalk noise, attenuation and receiver sensitivity of optical interconnect, and analyze its performance from the aspects of energy consumption, bandwidth density and latency. All the formulations are general to different technologies. 3.1 CROSSTALK NOISE The micro-resonator (MR) is an important device in optical interconnect. r 2 and k 2 are the power splitting ratios of the coupler between the ring and waveguide. We assume r 2 + k 2 = 1. Besides, a is the round trip attenuation of the ring. The ratio of the drop port power to the input port power is the function of light wavelength, and is expressed in Equation 1. T d (λ) = (1 r 2 ) 2 a 1 2r 2 a cosθ(λ) + r 4 a 2 (1) Here phase shift θ(λ) is the function of working frequency λ, which is expressed in Equation 2. Besides, n e is the effective refractive index of the ring, and R is the radius of the ring. θ(λ) = 4π 2 n e R/λ (2) At resonance wavelength λ n, the value of T d is maximized, and we use this property to filter signal λ n out of multiple signals in one waveguide. However, there will be small fraction of other signals appearing on drop port. The crosstalk noise coefficient in optical interconnect is the summation of these signals, and is expressed in Equation 3. ε o =... + T d (λ n 1 ) + T d (λ n+1 ) + T d (λ n+2 ) +... (3) Suppose there are m different wavelengths in the WDM optical system. The spacing between two neighboring wavelengths is λ. In worst case, n equals to m/2, and the maximum crosstalk coefficient is expressed in Equation 4. m o /2 ε o = 2 T d (λ n + i λ) (4) i=1 3.2 ATTENUATION The attenuation A is the ratio of the received optical power to the transmitted power. It mainly includes the coupling loss of optical pins, the passing by and insertion loss of micro-resonators, and the attenuation of waveguides or fibers. It is expressed in Equation (5). A o = η 2 o e α ol L 2 p (m o 1)T 2 d (λ n) (5) Here η is the coupling efficiency of each optical pin. α is the attenuation coefficient of waveguide, and L is the interconnect length. Besides, L p (n) is the passing by loss, and T d (λ) is the insertion loss of one micro-resonator. There is one micro-resonator inserted after the laser and another one before the photodetector. Optical signals will be attenuated if they pass by 7

8 micro-resonators. Signal λ n will be attenuated by a sequence of micro-resonators, whose resonance wavelength ranges from λ 0 to λ n 1. The ratio of the pass port power to the input port power is the function of light wavelength, and is expressed in Equation (6). T p (λ) = r 2 a 2 2r 2 acosθ + r 2 1 2r 2 a cosθ(λ) + r 4 a 2 (6) At their resonance wavelength, the value of T p is minimized. At other wavelength, the attenuation factor is close to one. T p (λ) is the frequency spectrum of micro-resonator with resonance wavelength λ n, and λ is the spacing between two neighboring wavelengths. The total passing by loss is expressed in Equation (7). In worst case, n equals to m 1. L p (n) = n T p (λ n + i λ) (7) i=1 3.3 RECEIVER SENSITIVITY The sensitivity of optical receiver is the minimum optical modulation amplitude (OMA) required in the receiver end. Suppose the noise is Gaussian distributed with standard deviations σ. If the signal to noise ratio equals to SNR, the logic 1 and logic 0 voltage levels are ± 1 2 SNR σ away from the theoretical decision point in the middle. We open the theoretical decision point by at least double the threshold voltage V th of the limiting amplifier (LA). The OMA is expressed in Equation (8). Here i n is the input referred RMS noise density of the transimpedance amplifier (TIA), f is the frequency of optical modulated signal, Z ti a is the transimpedance, and ρ is the responsivity of photodetector (PD). OMA = i n f 0.5 SNR + 2V th Z 1 ti a ρ (8) 3.4 ENERGY CONSUMPTION The total power consumption can be expressed in Equation (9). Here I mod and I bi as are the supply current and bias current of laser driver, I ti a and I l a are the supply current of the transimpedance amplifier and the limiting amplifier. We use two different supply voltages. V l and V c are the supply voltage of lasers and electrical circuits. P o = (I mod + I bi as )V l + (I ti a + I l a )V c (9) Parameter ε is the crosstalk noise coefficient. Extinction ratio r e is defined as the power ratio between logic level 0 and logic level 1. The minimum required eye amplitude in optical interconnect is 1 - ε - r e, which corresponds to OMA, the sensitivity of optical receiver. The maximum driving current required from the laser is the summation of supply current and bias current, and it is expressed in Equation (10). Here A is the attenuation of the entire optical interconnect. η s and I th are the slope efficiency and threshold current of laser diode. I mod + I bi as = OMA A o (1 ε o r e )η s + I th (10) 8

9 The supply current of transimpedance amplifier is proportional to the input pole of the transimpedance amplifier, and it is expressed in Equation (11). Here f is the working frequency of the transimpedance amplifier, C pd is the capacitance of photodetector, and V is the saturation voltage of the transistor in transimpedance amplifier. I ti a πf C pd V (11) We evaluate the energy consumption, which is defined as the energy consumed by the interconnects when they transmit unit bits of information. It is expressed in Equation (12). Here P is the power consumption of optical signal. The signal bandwidth is 2f. Each signal does not interfere with other signals in the same waveguide. Power P Energy Consumption = 2 Frequency f (12) 3.5 BANDWIDTH DENSITY The number of signals in one interconnect equals the free spectral range (FSR) divided by the spacing between two neighboring wavelengths. FSR is defined as the spacing between two successive resonance peaks in drop port spectrum, and its value is expressed in Equation (13). Here λ is the optical signal wavelength. R is the radius of micro-resonator, and n e is the effective refractive index of the waveguide in the micro-resonator. λ2 FSR = 2πn e R (13) The bandwidth of each optical interconnect equals the transmission bandwidth of one optical signal multiplied by the number of signals in one interconnect, and it is expressed in Equation (14). Here λ is the wavelength spacing between two neighboring signals. f is the modulation frequency of the optical signal so that the bandwidth is 2f. B o = 2 FSR f (14) λ At the bottom of the package, there are a grid of pins. The area bandwidth density is defined as the maximum bandwidth in unit area, and is expressed in Equation (15). Here B is the bandwidth of a single interconnect, and S = l h l w is the area of the optical pin. Area Density = Bandwidth B Area S (15) At each layer of the board, there are parallel interconnects. The linear bandwidth density is defined as the maximum bandwidth in unit width, and is expressed in Equation (16). Here B is the bandwidth of each interconnect, and p is the interconnect pitch. Linear Density = Bandwidth B Pitch p (16) 9

10 3.6 LATENCY We assume that the signal has a long pulse with narrow bandwidth, and ignore its nonlinear effects. The speed of optical signal is hence determined by its group velocity, with which the envelope of a pulse propagates in the optical medium. The latency is expressed in Equation (17). Here c is the light speed in vacuum. n g is the group reflection index. v o = c n g (17) In addition to the propagation delay, the parasitic capacitances of these electrical modules will also generate RC delays, whose values could not exceed one bit period 1/2f. The interconnect latency is expressed in Equation (18). Here L is the interconnect length, v is the signal propagation speed, and τ RC is the RC delay of electrical modules. Latency = Length L Speed v + Delay τ RC (18) 3.7 NOTATION TABLE The relationship between the notations in this section and the parameter/configuration name in OEIL are listed in Table 1. laser_slope_efficiency η s laser_threshold_current I th laser_extinction_ratio r e laser_voltage V l driver_voltage V c optical_pin_loss η o optical_pin_height l h optical_pin_width l w propagation_loss α wg_refractive_index n g wg_pitch p o signal_to_noise_ratio SNR tia_noise_density i n tia_transimpendance Z ti a la_voltage_threshold V th pd_responsity ρ pd_capacitance C pd mr_radius_range R mr_attenuation a mr_power_split_k k mr_refractive_index n e data_rate_optical 2 f length_optical L number_of_wavelengths m o laser_wavelength λ Table 1: The mapping between notations and optical parameter/configuration 10

11 4 MODELS FOR ELECTRICAL INTERCONNECT We build models for the crosstalk noise, attenuation and receiver sensitivity of electrical interconnect, and analyze its performance from the aspects of energy consumption, bandwidth density and latency. All the formulations are general to different technologies. 4.1 CROSSTALK NOISE In electrical interconnects, the crosstalk coefficient is defined as the ratio of noise amplitude to signal amplitude. Compared with single-ended traces, the crosstalk noise in differential traces is relatively small. The near-end crosstalk noise (NEXT) among parallel traces on board is the main source of crosstalk noise. This is because for properly terminated low-loss striplines, the far-end crosstalk noise (FEXT) is relatively very low. We define c(d) to be the crosstalk coefficient between two parallel traces with distance d, and it is expressed in Equation 19. c(d) = H 2 /(4d 2 + H 2 ) (19) In Equation 19, H is the distance between two metal layers. Parallel differential traces on the PCB board are analyzed. The crosstalk coefficient between the differential pair n and n + i is expressed in Equation 20. N d (i ) = c( i p e 2w) 2c( i p e ) + c( i p e + 2w) (20) The victim trace pair n has two traces in opposite directions and the aggressor trace pair n 1 also has two traces in opposite directions. Therefore, the crosstalk coefficient between two trace pairs is the summation of four terms. Apart from trace pair n 1, there are other aggressor trace pairs, such as n+1 and n+2. The total coefficient ε e is expressed in Equation 21. ε e =... + N d ( 1) + N d (1) + N d (2) +... (21) It is assumed that there are m e parallel trace pairs on the PCB board. The trace pair located in the middle of those trace pairs has the the largest crosstalk noises, and its crosstalk coefficient is expressed in Equation 22. m e /2 ε e = 2 N d (i ) (22) i=1 4.2 ATTENUATION In electrical interconnects, trace attenuation A e is the ratio of output signal amplitude to input signal amplitude, and is expressed in Equation (23). α e is the attenuation coefficient of trace, L is the interconnect length. Additionally, η e is the attenuation of each electrical pin, and there are two pins in a single electrical interconnect. A e = η 2 e e α e L (23) The attenuation coefficient α e is expressed in Equation (24), where the first and second terms are called skin effect loss and dielectric loss, respectively. In striplines, w and h are width and 11

12 height of trace. R dc is the direct current resistance, Z 0 is the characteristic impedance, and C 0 is the capacitance per unit length. t anδ D is the loss tangent in dielectric material. Their values will be discussed in Section VI. Additionally, f s is the frequency when skin depth equals half of trace height h. f is the working frequency of the signal. The attenuation coefficient is increased if f is increased. α e = R dc(w + h) 2Z 0 w ( f f s ) πf C 0 t anδ D Z 0 (24) The current in electrical interconnects will drive the electrical pins on both side of the trace. After infinite time, the voltage on the pin will be driven to the full swing voltage. However, for each bit signal, the time to drive the pin is half of the period 1/f. The ratio of the voltage after that given time to the full swing voltage is defined as the attenuation of each pin η e, and it is expressed in Equation (25). To drive the pin, current will be attenuated by resistance Z 0 and capacitance C p of electrical pin. η e = 1 e 1 2Z 0 Cp f (25) 4.3 RECEIVER SENSITIVITY In electrical interconnects. The driver injects currents through the pair of differential traces, and induces a voltage difference between the two ports of limiting amplifier. Only when this voltage difference is less than V th or greater than V th, signals can be detected by the limiting amplifier. The sensitivity of electrical receiver is defined as double the threshold voltage V th of limiting amplifier. 4.4 ENERGY CONSUMPTION The total power consumption is expressed in Equation (26). Current I 0 is the supply current of the driver, I l a is the supply current of the limiting amplifier, and V c is the supply voltage of these two components. The supply voltage is V c. The value of I l a is approximately proportional to the working frequency of limiting amplifier. P e = (2I 0 + I l a )V c (26) The received electrical signal has two voltage levels named V 1 and V 0, which represent logic levels of 1 and 0. A e and ε e are the attenuation and crosstalk noise coefficient of electrical interconnect. Their values have been discussed in the previous section. ε c is called transmitter offset coefficient, which is defined as the ratio of offset amplitude to signal amplitude. The minimum required eye amplitude in electrical interconnects is A e - ε e - ε c, which corresponds to V th, the sensitivity of electrical receivers. The minimum supply current required from the driver is double the current I 0, which is expressed in Equation (27). Z d is the differential impendence between two inputs of the differential pair. I 0 = 2V th (A e ε e ε c )Z d (27) 12

13 We evaluate the energy consumption, which is defined as the energy consumed by the interconnects when they transmit unit bits of information. It is expressed in Equation (28). Here P is the power consumption of optical signal. The signal bandwidth is 2f. Each signal does not interfere with other signals in the same waveguide. Power P Energy Consumption = 2 Frequency f (28) 4.5 BANDWIDTH DENSITY In electrical interconnects, there is only one signal in each differential pair. Therefore, the bandwidth of each electrical interconnect equals double the frequency, 2 f. If the signal frequency is increased, trace attenuation is increased. The value of coefficient margin ε, expressed in Equation (29), will be decreased. It is possible that these signals will not be detected by receiver because of noises. Every receiver has a minimum required coefficient margin, and the signal frequency of electrical interconnects is limited. Parameters ε e and ε c have been discussed in the previous subsection. A ε e ε c = ε (29) In Equation (29), ε is the coefficient margin, which is assumed to be 0.01 in this model. As mentioned in the previous section, the attenuation coefficient α e is the function of working frequency f, and this relationship could be expressed as α e = A (f ). Function A is a monotonically increasing function, and its inverse function is A 1. The maximum bandwidth of a single electrical interconnect is the function of trace length, which is expressed in Equation (30). It can be seen that if the interconnect length is increased, the bandwidth of electrical interconnects will be decreased. B e = 2A 1 ( ln(ε e + ε c + ε) ) (30) L At the bottom of the package, there are a grid of pins. The area bandwidth density is defined as the maximum bandwidth in unit area, and is expressed in Equation (31). Here B is the bandwidth of a single interconnect, and S = l h l w is the area of the optical pin. Area Density = Bandwidth B Area S (31) At each layer of the board, there are parallel interconnects. The linear bandwidth density is defined as the maximum bandwidth in unit width, and is expressed in Equation (32). Here B is the bandwidth of each interconnect, and p is the interconnect pitch. Linear Density = Bandwidth B Pitch p (32) 13

14 4.6 LATENCY In stripline design, copper traces on the PCB board are surrounded by dielectric material. When an electrical signal propagates along the trace, its speed is determined by the speed of a changing electric and magnetic field, which is in fact the speed of light in the material. The propagation speed of electrical signals is related to the relative dielectric constant of that material, and is expressed in Equation (33). c is the light speed in vacuum, which is about 12 inches per nanosecond. ɛ r is the relative dielectric constant of the material in the PCB board, and the values of ɛ r are different in different PCB boards. The signal speed is inversely proportional to the square root of relative dielectric constant. v e = c ɛr (33) In addition to the propagation delay, the parasitic capacitances of these electrical modules will also generate RC delays, whose values could not exceed one bit period 1/2f. The interconnect latency is expressed in Equation (34). Here L is the interconnect length, v is the signal propagation speed, and τ RC is the RC delay of electrical modules. Latency = Length L Speed v + Delay τ RC (34) 4.7 NOTATION TABLE The relationship between the notations in this section and the parameter/configuration name in OEIL are listed in Table 2. pcb_layer_height H pcb_trace_width w pcb_trace_height h pcb_trace_pair_pitch p e pcb_loss_tangent t anδ D pcb_dielectric ɛ r package_pin_pitch Se trace_half_depth_f f s trace_characteristic_z Z 0 trace_unit_length_c C 0 trace_direct_current_r R dc trace_input_impendance Z d electrical_pin_load_c C p la_threshold_voltage V th la_offset_coefficent ɛ c la_coefficent_margin ɛ circuit_voltage V c data_rate_electrical 2 f length_electrical L number_of_pairs m e number_of_stack_dies m d Table 2: The mapping between notations and electrical parameter/configuration 14

15 5 MODELS FOR SERIALIZERS AND DESERIALIZERS We build models for the energy efficiency, area and latency of serializers and deserializers. The SerDes models are integrated in both optical interconnects and electrical interconnects. All the formulations are general to different technologies. 5.1 SERDES MODELLING In E-O interfaces(fig. 2) the multiplexer blocks are important components, which select one of several input signals and forward the data from selected input port to output port. The basic multiplexer block has two inputs and one output. To store the bits of information during each clock cycle, three flip-flops are implemented. Clock signals are used to select input signals. In this design, input 0 is selected when clock signal is low, and input 1 is selected when clock signal is high. Multiplexer blocks in different stages are connected to different frequencies. A 1/2 clock divider is implemented in each stage to provide clock signals with different speeds. An array of microresonators are implemented along the waveguide to modulate N different optical wavelengths. Each microresonator has a unique resonance wavelength, and belongs to one of the E-O interfaces. In a basic multiplexer block, the output signal is delayed. In O-E interfaces(fig. 2), the demultiplexer blocks select one of several output signals and forward the data from input port to selected output port. which has one input and two outputs. Similarly, three flip-flops are implemented in demultiplexer blocks to store the bits of information. Clock signals are used to select output signals. In this design, output 0 is selected at the rising clock edge, and output 1 is selected at the falling clock edge. A 1/2 clock divider is implemented in each stage to provide clock signals with different frequencies. In optical WDM systems, each microresonator has a unique resonance wavelength, and belongs to one of the O-E interfaces. In a basic demultiplexer block, one of two parallel output signals is delayed. In0 In1 In2 In3 Out0 Out1 Out2 Out tb 2tb 6tb :1 Mux 2:1 Mux 1/4tb 1:2 Demux 1:2 Demux 1/4tb 2tb 2tb /2 Divider 2tb /2 Divider 2:1 Mux 1/2tb 1:2 Demux 1/2tb 3tb Driver Clock Generator Amplifer Clock Source Wavegudie PD Wavegudie Laser MR Output Input MR Figure 2: Basic Structures of E-O interface and O-E interface. 15

16 5.2 ENERGY EFFICIENCY AND AREA It is assumed that I o is the supply current of a single gate running at full clock speed, and the supply currents of other gates are scaled by their working frequencies. Therefore, the supply current of each component in multiplex blocks can be expressed in the unit I o. Table 3 shows the current breakdown of basic multiplexer blocks. The supply currents of multiplexers, flip-flops, and clock dividers running at full speed are 1I o, 1I o and 2I o, respectively. In R:1 E-O interface, the total current consumed by multiplexer blocks are about 5log 2 R I o. Assuming supply voltages are fixed, the power consumption of each component is proportional to the supply current I o. All of them can be expressed in the unit P e, which is the power consumption of a single gate. Table 4 shows the current breakdown of basic demultiplexer blocks. In 1:R O-E interface, the total current consumed by demultiplexer blocks are about 4log 2 R I o. P e = I 0 (2f ) V dd S e = S 0 (2f ) (35) It is assumed that S e is the area of a single gate running at full clock speed, and the areas of other gates are scaled by their working frequencies. The area breakdown of multiplexer blocks is similar to current breakdown. In R:1 E-O interface and 1:R O-E interface, the areas are about 5log 2 R S e and 4log 2 R S e, respectively. Power consumptions and areas of multiplexer blocks in both interfaces are summarized in Table 5, where unit power consumption P e and unit area S e are expressed in Equation 35. Component 4:1 Serializer 8:1 Serializer 16:1 Serializer R:1 Serializer Multiplexer l og 2 R Flip-flop l og 2 R Clock Divider /R Total (I 0 ) l og 2 R Table 3: Current Breakdown of Serializer Component 1:4 Deserializer 1:8 Deserializer 1:16 Deserializer 1:R Deserializer Flip-flop log 2 R Clock Divider /R Total (I 0 ) log 2 R Table 4: Current Breakdown of Deserializer E-O (P e ) E-O (S e ) O-E (P e ) O-E (S e ) Interface 5log 2 R 5log 2 R 4log 2 R 4log 2 R Table 5: Comparison of Power Consumption P e and Area S e 16

17 Power consumption of driver is denoted as P d. Each time the voltage level of PN junction is reversed, it is charged or discharged by the driver, where energies are consumed. On the other hand, power consumption of microresonator is denoted as P m. When voltage level of PN junction is high, it is forward biased, energies are consumed because of the direct current flowing through the PN junction. Power consumptions P d and P m are expressed in Equation 36. The dynamic driver power consumption is 1/4. The static microresonator power is 1/2. P d = 2f C m V 2 m P m = I m V m (36) P d is function of data rate f. C m is the input capacitance of microresonator. V m is the supply voltage of microresonator. P m, on the other hand, is not function of data rate f. I m is the direct current of microresonator. The area of each transmitter module S m in E-O interface is related to the size of microresonator. Besides, S l is the area of each on-chip laser. 5.3 LATENCY The latency of inter-chip interconnects is the amount of time it takes for the head of signals to travel from end to end. It includes three parts: the multiplexer/demultiplexer delay, the RC delay and the propagation delay. It is assumed that the bit time of serial optical signals is t b and the propagation delay is t p. Latencies of E-O interface and O-E interface are denoted as T eo and T oe, and expressed in Equation 37. The multiplexer delay in E-O interfaces are (R-1) t b. The average demultiplexer delay in O-E interfaces are (R-1) t b. On the other hand, the RC delays in all interfaces are assumed to be t b. T eo =Rt b + t p T oe = Rt b + t p (37) The total latency is the summation of multiplexer/demultiplexer delay, RC delay and propagation delay. t b is expressed as 1/f, where f is the data rate of serial optical signals. t p is expressed as nl/c, where n is the refractive index of optical interconnect. c is the light speed in vacuum, and L is the length of optical waveguide. R is the parallel-to-serial ratio of interfaces. 5.4 NOTATION TABLE The relationship between the notations in this section and the parameter/configuration name in OEIL are listed in Table 6. serdes_ratio_optical R serdes_ratio_electrical R serdes_cur_optical I o serdes_cur_electrical I o serdes_area_optical S 0 serdes_area_electrical S 0 laser_area S l mr_area S m mr_tuning_power P t mr_static_power P m mr_dynamic_power P d /2f Table 6: The mapping between notations and SerDes circuit 17

18 REFERENCES [1] Optical and Electrical Interfaces and Links (OEIL). [Online]. Available: ust.hk/~eexu. [2] Z. Wang, J. Xu, P. Yang, X. Wang, Z. Wang, L. H. Duong, Z. Wang, H. Li, R. K. Maeda, X. Wu, Y. Ye, and Q. Hao, Alleviate chip I/O pin constraints for multicore processors through optical interconnects, in Design Automation Conference (ASP-DAC), th Asia and South Pacific, Jan VERSION HISTORY Revision Date Author(s) Description 1.0 DEC, 2014 Zhehui Wang, Jiang Xu, Peng Yang, Internal released Zhifei Wang, Luan Huu Kinh Duong, Xuan Wang, Zhe Wang, Haoran Li, Rafael Kioji Vivas Maeda 2.0 AUG, 2015 Zhehui Wang, Jiang Xu, Peng Yang, Basic analytical model Zhifei Wang, Luan Huu Kinh Duong, Xuan Wang, Zhe Wang, Haoran Li, Rafael Kioji Vivas Maeda 3.0 DEC, 2015 Zhehui Wang, Jiang Xu, Peng Yang, Add SerDes analyses Zhifei Wang, Luan Huu Kinh Duong, Add area analyses Xuan Wang, Zhe Wang, Haoran Li, Rafael Kioji Vivas Maeda 18